This disclosure relates generally to the field of radar signal processing, and more particularly to an approach for determining an angle of arrival of a radar signal received from an emitter.
Angle of Arrival (AOA) determination requires an accurate description of the antenna performance over azimuth or elevation angle while avoiding ambiguity. Currently, the standard industry practice is to curve fit the antenna radiation pattern using one of three approaches: pure Gaussian, bi-faceted Gaussian, and Polynomial. One criterion by which radar receivers, such as Radar Warning Receivers, are evaluated is the Root Mean Square (RMS) angular error, which is principally determined by the quality of the radiation pattern and the curve fit. Although prior fitting approaches have been somewhat successful in the past, none have provided a ubiquitous, optimized solution. Accordingly there is a need for a fitting approach that provides a more accurate radiation pattern representation with a smaller RMS error, no ambiguity, and generic pattern fitting capability.
In accordance with an example, a method for determining an angle of arrival of a radar signal received from an emitter is provided. The method includes, in a radar receiver system, given a radiation pattern of an antenna receiving a radar signal from an emitter, in an initial iteration, representing an approximation of the pattern as plurality of windows. Each window is defined by two boundaries. Each of the boundaries having an azimuth angle value and an amplitude value. The approximation further includes an inflexion point. The inflexion point is a boundary having an amplitude value higher than the other boundaries. The method further includes for each of the boundaries, adjusting at least one of a respective azimuth angle value or amplitude value of a subject boundary. The method further includes generating a next approximation of the pattern based on the adjustment to the subject boundary. The method further includes comparing the next approximation to an approximation of the pattern generated in a prior iteration, which includes the initial approximation. The method further includes comparing a slope associated with a portion of the next approximation represented by each window to a non-zero threshold value. The method further includes determining whether the next approximation is constantly increasing on one side of the inflexion point and constantly decreasing on the other side of the inflexion point, and identifying the next approximation as an optimized monotonic fit based on the comparisons and determination. The method further includes calculating an angle of arrival of the radar signal received from the emitter based on the optimized monotonic fit.
In accordance with another example, a system for determining an angle of arrival of a radar signal received from an emitter is provided. The system includes memory having computer executable instructions thereupon and at least one interface receiving a radiation pattern of an antenna that receives a radar signal from an emitter. The system further includes an approximating engine coupled to the memory and the at least one interface. The computer executable instructions when executed by the approximating engine cause the approximating engine to in an initial iteration, represent an approximation of the pattern as plurality of windows. Each window is defined by two boundaries. Each of the boundaries having an azimuth angle value and an amplitude value. The approximation further includes an inflexion point. The inflexion point is a boundary having an amplitude value higher than the other boundaries. The approximating engine further caused to, for each of the boundaries, adjust at least one of a respective azimuth angle value or amplitude value of a subject boundary. The approximating engine further caused to generate a next approximation of the pattern based on the adjustment to the subject boundary. The detecting engine further caused to compare the next approximation to an approximation of the pattern generated in a prior iteration, which includes the initial approximation. The detecting engine further caused to compare a slope associated with a portion of the next approximation represented by each window to a non-zero threshold value. The detecting engine further caused to determine whether the next approximation is constantly increasing on one side of the inflexion point and constantly decreasing on the other side of the inflexion point, and identify the next approximation as an optimized monotonic fit based on the comparisons and determination. The detecting engine further caused to provide the optimized monotonic fit to a radar receiver coupled to the approximating engine. The radar receiver calculates an angle of arrival of the radar signal received from the emitter based on the optimized monotonic fit
In accordance with yet another example, a tangible computer-readable storage medium having computer readable instructions stored therein for determining an angle of arrival of a radar signal received from an emitter is provided. The computer readable instructions when executed by one or more processors cause the one or more processors to, given a radiation pattern of an antenna receiving a radar signal from an emitter, in an initial iteration, represent an approximation of the pattern as plurality of windows. Each window is defined by two boundaries. Each of the boundaries having an azimuth angle value and an amplitude value. The approximation further includes an inflexion point. The inflexion point is a boundary having an amplitude value higher than the other boundaries. The one or more processors further caused to, for each of the boundaries, adjust at least one of a respective azimuth angle value or amplitude value of a subject boundary. The one or more processors further caused to generate a next approximation of the pattern based on the adjustment to the subject boundary. The one or more processors further caused to compare the next approximation to an approximation of the pattern generated in a prior iteration, which includes the initial approximation. The one or more processors further caused to compare a slope associated with a portion of the next approximation represented by each window to a non-zero threshold value. The one or more processors further caused to determine whether the next approximation is constantly increasing on one side of the inflexion point and constantly decreasing on the other side of the inflexion point, and identify the next approximation as an optimized monotonic fit based on the comparisons and determination. The one or more processors further caused to provide the optimized monotonic fit to a radar receiver coupled to the approximating engine. The radar receiver calculates an angle of arrival of the radar signal received from the emitter using the optimized monotonic fit.
In some examples, any of the aspects above can include one or more of the following features.
In other examples of the method, adjusting includes increasing or decreasing the azimuth angle value of the subject boundary by a fixed value.
In some examples of the method, adjusting includes randomizing the amplitude value of the subject boundary by a random value.
Other examples of the method further include calculating the random value based on a normal distribution having a mean value equal to that of the given radiation pattern and a standard deviation. The standard deviation is dependent on a magnitude of divergence of the approximation generated in the prior iteration and the given radiation pattern.
In some examples of the method, comparing the next approximation of the pattern further includes computing a least squares error for the next approximation, and selecting the next approximation when the computed least squares error for the next approximation is smaller than a least squares error for the approximation generated in a prior iteration.
In other examples of the method, comparing the slope includes determining whether the slope associated with each portion of the next approximation is greater than the non-zero threshold value.
In some examples of the method, identifying includes returning, as the optimized monotonic fit, the next approximation having a least squares error that is less than a threshold.
The method further includes adding a boundary between boundaries defining a window having a span of azimuth angle values greater than other windows.
In some examples of the method, identifying includes returning, as the optimized monotonic fit, the next approximation having a maximum number of boundaries added.
In some examples of the method, calculating the angle of arrival includes, given radiation patterns of two adjacent antennas, comparing a ratio of optimized monotonic fit of the radiation patterns and a ratio of an effective received power from each of two adjacent antennas and resolving the angle of arrival based on the comparison of ratios.
In other examples of the method, calculating the angle of arrival given adjacent antennas having a first radiation pattern and a second radiation pattern, populating a difference table, directly, with a ratio of a first optimized monotonic fit of the first radiation pattern and a second optimized monotonic fit of the second radiation pattern. The method further includes calculating the angle of arrival of the radar signal based on the difference table.
These and other features and characteristics, as well as the methods of operation and functions of the related elements of structure and the combination of parts and economies of manufacture, will become more apparent upon consideration of the following description and the appended claims with reference to the accompanying drawings, all of which form a part of this specification, wherein like reference numerals designate corresponding parts in the various Figures. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of claims. As used in the specification and in the claims, the singular form of “a”, “an”, and “the” include plural referents unless the context clearly dictates otherwise.